Hi David,
It's not completely intuitive but you can do the substitution in several
stages. In your example (this is run isympy where f and g are both
functions):
In [24]: eq = Eq(n**2*f(x) - x*Derivative(f(x), x) + (1 -
2*x)*Derivative(f(x), (x, 2)), 0)
In [25]: eq
Out[25]:
2
2 d d
n ⋅f(x) - x⋅──(f(x)) + (1 - 2⋅x)⋅───(f(x)) = 0
dx 2
dx
In [26]: eq.subs(f(x), g(cos(t)))
Out[26]:
2
2 d d
n ⋅g(cos(t)) - x⋅──(g(cos(t))) + (1 - 2⋅x)⋅───(g(cos(t))) = 0
dx 2
dx
In [27]: eq.subs(f(x), g(cos(t))).doit()
Out[27]:
2
n ⋅g(cos(t)) = 0
More substitutions are probably needed to continue from here.
Ideally sympy would have a function like maple's dchange:
https://www.maplesoft.com/support/help/Maple/view.aspx?path=PDEtools/dchange
https://github.com/sympy/sympy/issues/17590
Oscar
On Thursday, 19 November 2020 at 00:08:01 UTC [email protected] wrote:
> Dear Group,
>
> Suppose I have a differential equation such as:
>
> Eq(n^2*f(x) - x*Derivative(f(x), x) + (1 - 2*x)*Derivative(f(x), (x, 2)))
>
> (Though typically more complicated)
>
> and I want to replace the x variable - say x=cos(t)
>
> Is there a way to make that substitution within SymPy and get back a
> differential equation in t, as opposed to simply throwing the equation to
> dsolve and hoping that it will solve it?
>
> Likewise, is it possible to make a change of variable within an integral
> without simply letting integrate loose on it?
>
> David
>
>
>
>
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